Properties

Label 345.2
Level 345
Weight 2
Dimension 2771
Nonzero newspaces 12
Newform subspaces 35
Sturm bound 16896
Trace bound 1

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Defining parameters

Level: \( N \) = \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 35 \)
Sturm bound: \(16896\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(345))\).

Total New Old
Modular forms 4576 3019 1557
Cusp forms 3873 2771 1102
Eisenstein series 703 248 455

Trace form

\( 2771q + 5q^{2} - 19q^{3} - 35q^{4} - q^{5} - 65q^{6} - 36q^{7} + 9q^{8} - 23q^{9} + O(q^{10}) \) \( 2771q + 5q^{2} - 19q^{3} - 35q^{4} - q^{5} - 65q^{6} - 36q^{7} + 9q^{8} - 23q^{9} - 61q^{10} + 20q^{11} - 17q^{12} - 26q^{13} + 24q^{14} - 41q^{15} - 187q^{16} - 30q^{17} - 105q^{18} - 76q^{19} - 79q^{20} - 124q^{21} - 148q^{22} - 65q^{23} - 155q^{24} - 111q^{25} - 50q^{26} - 85q^{27} - 164q^{28} - 10q^{29} - 76q^{30} - 144q^{31} - 15q^{32} - 40q^{33} - 74q^{34} - 36q^{35} - 101q^{36} - 162q^{37} - 152q^{38} - 100q^{39} - 233q^{40} - 66q^{41} - 218q^{42} - 184q^{43} - 232q^{44} - 45q^{45} - 415q^{46} - 144q^{47} - 213q^{48} - 237q^{49} - 39q^{50} - 132q^{51} - 390q^{52} - 14q^{53} - 21q^{54} - 134q^{55} - 100q^{56} - 16q^{57} - 178q^{58} - 20q^{59} + 60q^{60} - 66q^{61} + 96q^{62} + 96q^{63} + 69q^{64} + 18q^{65} + 88q^{66} + 130q^{68} + 111q^{69} - 108q^{70} + 88q^{71} + 251q^{72} + 10q^{73} + 50q^{74} + 3q^{75} - 204q^{76} - 80q^{77} - 64q^{78} - 140q^{79} - 165q^{80} - 243q^{81} - 162q^{82} - 116q^{83} - 142q^{84} - 272q^{85} - 300q^{86} - 260q^{87} - 16q^{88} - 162q^{89} - 215q^{90} - 416q^{91} - 235q^{92} - 276q^{93} - 368q^{94} - 98q^{95} - 255q^{96} - 82q^{97} - 19q^{98} - 222q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
345.2.a \(\chi_{345}(1, \cdot)\) 345.2.a.a 1 1
345.2.a.b 1
345.2.a.c 1
345.2.a.d 1
345.2.a.e 1
345.2.a.f 1
345.2.a.g 2
345.2.a.h 2
345.2.a.i 2
345.2.a.j 3
345.2.b \(\chi_{345}(139, \cdot)\) 345.2.b.a 2 1
345.2.b.b 2
345.2.b.c 6
345.2.b.d 14
345.2.c \(\chi_{345}(206, \cdot)\) 345.2.c.a 16 1
345.2.c.b 16
345.2.h \(\chi_{345}(344, \cdot)\) 345.2.h.a 4 1
345.2.h.b 8
345.2.h.c 8
345.2.h.d 24
345.2.i \(\chi_{345}(47, \cdot)\) 345.2.i.a 4 2
345.2.i.b 4
345.2.i.c 80
345.2.j \(\chi_{345}(22, \cdot)\) 345.2.j.a 48 2
345.2.m \(\chi_{345}(16, \cdot)\) 345.2.m.a 30 10
345.2.m.b 30
345.2.m.c 50
345.2.m.d 50
345.2.n \(\chi_{345}(14, \cdot)\) 345.2.n.a 40 10
345.2.n.b 400
345.2.s \(\chi_{345}(11, \cdot)\) 345.2.s.a 160 10
345.2.s.b 160
345.2.t \(\chi_{345}(4, \cdot)\) 345.2.t.a 240 10
345.2.w \(\chi_{345}(7, \cdot)\) 345.2.w.a 480 20
345.2.x \(\chi_{345}(2, \cdot)\) 345.2.x.a 880 20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(345))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(345)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)